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In BL models however, magnetic buoyancy not only removes ﬂux from the overshoot layer but also contributes directly to the poloidal ﬂux production procedure by transporting the strong toroidal ﬁeld to the surface, thus playing a more signiﬁcant role.

Characteristics Of A Magnetic Buoyancy Driven Solar Dynamo Model

In Figure 5 (Top Panel) we present a plot of the variation of the toroidal ﬁelds within the overshoot layer with varying B0, for fb = 0.05.

Characteristics Of A Magnetic Buoyancy Driven Solar Dynamo Model

So we ﬁx Bc at 105 G and study the variation of the toroidal ﬁeld within the overshoot layer with fb in Figure 6.

Characteristics Of A Magnetic Buoyancy Driven Solar Dynamo Model

Consequently, overshooting of density will be unable to prompt gravitational instabilities in 1D experiments, but it may be important in more than 1D (e.g., Schwarz et al. 1972; Kang et al. 2000).

The nonlinear development of the thermal instability in the atomic ISM and its interaction with random fluctuations

Consequently, the supersonic crushing process is more violent than in DEN15, causing a large density overshoot, of roughly 30 × ρisob .

The nonlinear development of the thermal instability in the atomic ISM and its interaction with random fluctuations

Clouds undergo an overshoot of density in the crushing stage (not shown).

The nonlinear development of the thermal instability in the atomic ISM and its interaction with random fluctuations

Overshooting in the stable envelope is more prominent near the poles, as in the right panel showing latitudinal cuts as a function of radius.

Looking Deep Within an A-type Star: Core Convection Under the Influence of Rotation

Decreasing the viscosity of the ﬂow leads to a smaller overshooting region.

Looking Deep Within an A-type Star: Core Convection Under the Influence of Rotation

As explained in paper V, this particular situation, at the limit where the loops generally disappear, results from the higher luminosity of the model having the more massive He–cores (either as a result of overshooting or as a result of rotation).

Interestingly a similar conclusion could be reached based on the results of our paper V, and this shows that the present results depend weakly on overshooting or on the inclusion of the effects of horizontal turbulence in the coeﬃcient of shear diffusion.

The uniform upper bound can easily be extended to all z ∈ C 2n using strong Markov property and overshoot estimate (10).

The Beurling estimate for a class of random walks

Hence one expects (also using an easy overshoot argument) O(log n) “excursions” from C 4n \ C 2n into C n before leaving Cm, and for each such excursion there is a positive probability, conditioned on the past of the walk, that the random walk visits [k, n]κ during that excursion due to Lemma 7.